LESSON 2 :
PROJECTILE MOTION: A TWO
DIMENSIONAL MOTION
FOCUS POINTS:
Describe the horizontal and vertical motions of a
projectile.
Investigate the relationship between the angle of
release and the height and range of the projectile.
PROJECTILE MOTION
Is the path followed by a ball when you
throw it and it falls to the ground.
PROJECTILE
Is an object that is initially thrown into the air and
continues to move on its trajectory acted upon by
the gravity.
You will understand what is happening to the
projectile by analyzing its velocity as its travels its
trajectory.
Elements of Projectile Motion
When launching the projectile, it is given by an
initial velocity, at an initial angle. As it travels
through the air, it displaces in two dimensions,
along the horizontal, and along the vertical.
What goes up, returns back to earth and hits
the earth or a target with a final velocity.
We usually solve for three factors in projectile
motion:
Pro Elem • time of flight – the entire duration while the
jec ent
tile s o projectile is in its trajectory
Mo f
tio • Range – the maximum horizontal distance
n
travelled by the projectile.
• Maximum height – maximum vertical
displacement travelled by the projectile in its
trajectory.
Through the Flight 1. We will neglect the effect of air resistance on the body.
2. We can separate the displacement and velocity to its x and y
components.
Along the Horizontal 1. The x component of the velocity is always constant throughout the
range.
2. the horizontal displacement (X) follows a linear motion.
Co jectil
Pro
nd
Along the Vertical 1. The y-component behaves as free-fall, and thus, only affected by
itio e Mo
the acceleration due to gravity.
ns
2. Since our velocity is usually in an upward direction, from 0 to less
than 90 degree with respect to the horizontal, then our convention is
of
upward positive, downward negative.
the
tio
3. Before reaching the maximum height, gravity acts against the
n
velocity, slowing it down until it reaches zero. This part is equivalent
to a p-t graph where velocity is positive, but acceleration is negative.
4. After reaching the maximum height, gravity is in the same direction
as the velocity, speeding up.
When the 1. The x component of the velocity is
Co Vertical always constant.
Pr ndi Displaceme 2. The y component of the velocity is
oje tio
cti ns nt is at its zero.
le of Maximum 3. the acceleration is still (g) and not
M th
oti e zero.
on
KINEMATICS BIG THREE
EQUATIONS
•d= vit+1/2at2 Wherein:
D= distance in m
•Vf = vi+at Vf= Final Velocity in m/s
Vi= Initial Velocity in m/s
•(Vf ) 2 = (vi) 2+2ad A= acceleration m/s 2
An airplane accelerates
Ex down a runway at 3.
am
pl 20m/s^2 for 32.8 s until is
e
#1
: finally lifts off the ground.
Determine the distance
traveled before it take off.
A car starts from rest and
Exa
mp accelerates uniformly over a
le
#2
: time of 5.21s for a distance
of 110m. Determine the
acceleration of the car.
A feather is dropped on the
Exa moon from a height of
mp 1.40metes. The acceleration of
le gravity on the moon is
#3
:
1.67m/s^2. determine the time
for the feather to fall to the
surface of the moon.
Upton Chuck is riding the
Exa Giant Drop at Great
mp
le America. If Upton free
#4
: falls for 2.60seconds, what
will be his final velocity
and how far will he fall?
A race car accelerates
Exa uniformly from 18.5 m/s
mp
le to 46.1m/s in 2.47
#5
: seconds. Determine the
acceleration of the car
and the distance traveled.
Rocket- powered sled are used to
test the human response to
Exa acceleration. If a rocket- powered
mp
le sled is accelerated to a speed of
#6
: 444 m/s in 1.83 seconds, then
what is the acceleration and
what is the distance traveled by
the sleds?
